As a general matter, CAD systems require a constraint server for geometric modeling purposes. Most CAD constraint servers are specialized for geometric modeling purposes and do not handle general mathematical relationships. In addition, most conventional CAD CS's are parametric with some limited variational capabilities. Several geometric problems are not easily solved with parametric methods, so designers and users of conventional constraint servers attempt to adapt them to solve these modeling problems on a special-case basis.
The special cases employ methods that are somewhat variational, but not in a broad sense of the term. Instead, the adapted functionality is somewhat analogous to the goal seeking capability of a spreadsheet. A spreadsheet is basically parametric, but with a limited ability to solve systems of equations through the use of goal seeking methods.
It would be useful to provide a system utilizing true variational methods to enable enhanced handling and solving of geometric and other problems in CAD and other design and modeling systems.
It would also be useful to provide a system that can handle general mathematical as well as geometric constraints in an integrated manner.
In addition, it would be useful to provide a system that combines mathematical and geometric modeling in a manner that eliminates performance and convergence problems, and simplifies customer modeling.
Still further, it would be useful to provide a system that supports flexible dependent instances (non-rigid bodies) with inherent functional properties, thus providing users with the ability to model devices that move and/or respond in some manner when assembled as dependent instances with other simulated parts.